Simplify the following expression: $ n = \dfrac{-5}{3} - \dfrac{-6}{-3y + 4} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-3y + 4}{-3y + 4}$ $ \dfrac{-5}{3} \times \dfrac{-3y + 4}{-3y + 4} = \dfrac{15y - 20}{-9y + 12} $ Multiply the second expression by $\dfrac{3}{3}$ $ \dfrac{-6}{-3y + 4} \times \dfrac{3}{3} = \dfrac{-18}{-9y + 12} $ Therefore $ n = \dfrac{15y - 20}{-9y + 12} - \dfrac{-18}{-9y + 12} $ Now the expressions have the same denominator we can simply subtract the numerators: $n = \dfrac{15y - 20 + 18 }{-9y + 12} $ Distribute the negative sign: $n = \dfrac{15y - 20 + 18}{-9y + 12}$ $n = \dfrac{15y - 2}{-9y + 12}$ Simplify the expression by dividing the numerator and denominator by -1: $n = \dfrac{-15y + 2}{9y - 12}$